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Prime matrices and prime polynomials

Published online by Cambridge University Press:  01 August 2016

Alan F. Beardon
Alan F. Beardon*
Affiliation:
Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB
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Extract

In an earlier paper in the Gazette the authors of define what it means for a matrix in a set M of n × n matrices to be prime, namely if it is not the product of two matrices in M, neither of which is the identity. They then showed that there are exactly two primes in the set M2 of 2 × 2 matrices with non-negative integral entries and unit determinant, namely

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 528 , November 2009 , pp. 433 - 440
Copyright
Copyright © The Mathematical Association 2009

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References

1. Rivett, P. F. and Mackinnon, N. I. P., Prime matrices, Math. Gaz., 70 (December 1986) pp. 257–259.10.2307/3616179CrossRefGoogle Scholar
2. Ritt, J. F., Prime and composite polynomials, Trans. Amer. Math. Soc. 23 (1922) pp. 51–66.10.1090/S0002-9947-1922-1501189-9CrossRefGoogle Scholar